Scottyboy,
Bless you for caring about the 1 5/8" and bless you again for using fractions to describe the situation.
I'd dig the hole where I didn't hit the rock, but I'm an engineer. The accountant would probably get a bigger pick if there was a rock in the way.
I used to freak people out by doing the 70' or 80'*SQRT(2) in my head and then pacing it off to spot second base. Then some guy would come out with a rule book and a tape measure and I'd be spot on...
Then they promoted me to management and I forgot how to tie my shoes, frequently wet myself, speak in three word sentances, drool a lot, forget the names of my kids, co-workers, pets, etc.
Fortunately Jr has moved up to 90' fields where they always have a post. Now we spend 20 minutes with a shovel trying to find it, despite knowing the distance from home to second and having first and third to line up with...
Seriously, pace off the 113' 1 5/8" from HP (back point) as close to straight on from HP over the rubber and mound & make a mark (small arc). Then (in baseline) find 80' from the outside (foul line side) corner of third base to where you think second base should be and make a mark (another small arc). Do the same from first. Now you have three arks. If they're all intersect, go buy a lottery ticket, forgoing the rest of this exercise. If (more likely) they point of intersection is within 3"-1', pick the center and dig a hole. If there is a significant descrepancy instead, something isn't right. Step back and figure it out. If you can do the fraction thing, you can figure out that the foul lines aren't at a 90 degree angle, the mound is off center or some other mathmatical transgression was committed by the lowest bidder who won the job to lay out the field in the first place.
As a previous poster suggested, get it close and you'll be a fine.
I'm going back to trying to figure out who is winning the Duke (37)/Fl St. (29) game...